Rolling bearings enable low-friction movement under heavy loads in rotating machinery with applications ranging from industrial processes to wind turbines and vehicles. It is an accepted fact that even if all necessary operating conditions such as sufficient lubrication, proper alignment and a good surrounding environment are met, fatigue and mechanical wear of the contact surfaces bearings is unavoidable. Proper functionality of bearings is often critical and a breakdown can cause large economical loss or even pose a threat to personal safety. In heavy industrial processes such as steelmaking, the degradation can be quite rapid due to inherently harsh environments combined with severe loads.
To avoid unpredicted failures and enable planned maintenance, scheduled or continuous condition monitoring of a bearings state is standard practice where feasible. Vibration analysis is a common condition-monitoring technique in which the vibrations from a spinning bearing are measured with, a transducer and analysed on some digital processing platform, looking for signs of incipient or imminent damage. Contact surface defects create impulsive vibrations, occurring periodically as rolling elements strike developing pits or cracks in the bearing races. If sufficiently strong, these periodic impacts show up as peaks in the vibration signal's frequency spectrum which may then be matched to the bearing's characteristic frequencies, corresponding to each of the different expected faults (e.g. inner/outer race damage). The characteristic frequencies are calculated in advance from the bearing's dimensions and the axis rotation speed, see N. Tandon and A. Choudhury, “A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings,” Tribology international, vol. 32, pp, 469-480, August 1999. Vibration analysis can be done either by using a portable, hand-held instrument (scheduled monitoring) or with a permanently mounted system performing continuous trend monitoring.
The main challenge in performing successful vibration analysis is to detect and enhance the weak, impulsive vibrations associated with bearing defects in measured signals plagued by measurement noise and disturbing vibrations. Furthermore, the unknown and non-trivial transfer function between the fault-impulse sources (i.e. rolling elements striking surface defects) and the transducer results in phase and amplitude distortion that tends to obscure the vibration patterns of interest by reducing the signal's ‘peakiness’, see S. C Braun, “The signature analysis of sonic bearing vibrations,” IEEE Transactions on Sonics and Ultrasonics, vol. SU-27, pp, 317-328, November 1980. A signal pre-processing method is generally required to improve the signal quality beige the actual hearing condition assessment is made. Examples of such processing can be found in U.S. Pat. No. 6,868,348 B1 and U.S. Pat. No. 6,648,700 B1.
The shock pulse method (SPM) is a simple, widespread technique utilizing a vibration transducer with a tuned resonance frequency to detect the presence of fault-induced impulses in a bandpass frequency range around 32 kHz. This center frequency is selected to, in most cases, produce a high signal-to-noise ratio by making the transducer sensitive to fault impulses while filtering out lower frequencies, where most disturbing vibrations reside. A related, more advanced approach is the popular high-frequency resonance technique (HFRT), also called envelope analysis, in which a bandpass-filtered vibration signal is subject to envelope detection to reveal impulsive vibrations. Despite its popularity, HFRT is known to have issues with reliability, especially if the bearing damage is well progressed, (see N. Tandon and A. Choudhury, “A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings,” Tribology international, vol. 32, pp. 469-480, August 1999) and requires careful selection of the bandpass filter's center frequency depending on the measurement setting, see P. D. McFadden and J. D. Smith, “Vibration monitoring of rolling element bearings by the high-frequency resonance technique—a review,” Tribology international, vol. 17, pp. 3-40, February 1984. Also, the non-linear operations involved in envelope detection requires a high signal-to-noise ratio (SNR) for reliable results.
A different approach that avoids the use of specialized transducers or non-linear signal processing is to employ the principle of deconvolution. A linear, digital filter is used to compensate for the distorting transfer function between the fault-vibration source and the transducer so that any underlying impulses appear less distorted. Simple deconvolution examples for other applications can be found in U.S. Pat. Nos. 5,744,722 and 5,130,951. In the deconvolution technique, the measured vibration signal is modeled as a stochastic process and the transfer function as an unknown, linear system. The parameters of an adaptive deconvolution filter are then adjusted in an iterative algorithm to optimise the resulting output signal quality according to some statistical measure. Traditionally, kurtosis is employed as the statistical measure to maximize for deconvolution of hearing vibration signals, sec N. Sawalhi, R. B. Randall, and H. Endo, “The enhancement of fault detection and diagnosis in rolling element bearings using minimum entropy deconvolution combined with spectral kurtosis,” Mechanical systems and signal processing, vol. 21, pp. 2616-2633. August 2007, Kurtosis is defined as the normalized fourth moment of a random variable and reflects a signal's peakiness. The rationale is that the filter setting that maximizes the kurtosis of the output (i.e. maximizes its peskiness) also gives optimum transfer function distortion removal under the given conditions to enhance an underlying impulsive vibrations as much as possible.
While simple and intuitively attractive, deconvolution by maximizing kurtosis proves less useful in practice as the adaptive deconvolution filter is likely to amplify disturbing sinusoidal vibrations, which will therefore mask any weak impulsive vibrations and cause bearing defects to go un-detected. The reason for this is that the sinusoidal disturbances typically found in vibrations from rotating machines are not clearly distinguished from impulses in terms of their kurtosis value. While sinusoids may be suppressed with an adaptive, noise-cancelling filter prior to deconvolution, this increases not only the implementation cost but also the risk of accidentally cancelling defect signatures, see D. Ho and R. B. Randall, “Optimisation of bearing diagnostic techniques using simulated and actual bearing fault signals,” Mechanical signals and signal processing, vol. 14, pp. 763-788, September 2000.
More sophisticated processing techniques, such as wavelet-based methods and neural network algorithms have also been considered. While these may give decent reliability, they are far more computationally demanding and are thus only when power and processing capacity is abundant. This excludes compact, low-cost or energy-efficient solutions such as handheld devices and embedded processing systems.